As \(A_n\)  is torsion-free, Bredon homology with respect to the family of finite groups is in fact ordinary homology. The proposition is then obtained by applying Universal Coefficient Theorem [1]} to the ordinary homology groups of \(A_n\)  (Proposition REF ), taking into account that the latter are torsion-free and that the \(K\) -theory groups are abelian.
